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BEST PROXIMITY POINT THEOREMS FOR CYCLIC QUASI-CONTRACTION MAPS IN UNIFORMLY CONVEX BANACH SPACES

Part of: Connections with other structures, applications Nonlinear operators and their properties Spaces with richer structures

Published online by Cambridge University Press:  13 October 2016

NGUYEN VAN DUNG  and
VO THI LE HANG
NGUYEN VAN DUNG*
Affiliation:
Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam email [email protected]
VO THI LE HANG
Affiliation:
Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, 783 Pham Huu Lau Street, Ward 6, Cao Lanh City, Dong Thap Province, Viet Nam email [email protected]
*
✉ [email protected]
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Abstract

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In this paper we first give a negative answer to a question of Amini-Harandi [‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim.56 (2013), 1667–1674] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi for cyclic strongly quasi-contractions are true under weaker assumptions.

Keywords

cyclic quasi-contractionbest proximity pointuniformly convex Banach space

MSC classification

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Secondary: 54E05: Proximity structures and generalizations 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 1 , February 2017 , pp. 149 - 156
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Amini-Harandi, A., ‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim. 56 (2013), 1667–1674.CrossRefGoogle Scholar
Basha, S. S., Shahzad, N. and Jeyaraj, R., ‘Best proximity points: approximation and optimization’, Optim. Lett. 7(1) (2013), 145–155.CrossRefGoogle Scholar
Dung, N. V. and Hang, V. T. L., ‘Remarks on cyclic contractions in b-metric spaces and applications to integral equations’, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM (2016), 9 pages doi:10.1007/s13398-016-0291-5.Google Scholar
Dung, N. V. and Radenović, S., ‘Remarks on theorems for cyclic quasi-contractions in uniformly convex Banach spaces’, Kragujevac J. Math. 40(2) (2016), 272–279.CrossRefGoogle Scholar
Eldred, A. A. and Veeramani, P., ‘Existence and convergence of best proximity points’, J. Math. Anal. Appl. 323 (2006), 1001–1006.CrossRefGoogle Scholar
Gabeleh, M., ‘Best proximity point theorems via proximal non-self mappings’, J. Optim. Theory Appl. 164(2) (2015), 565–576.CrossRefGoogle Scholar
Karapinar, E., Du, W. S., Kumam, P., Petruşel, A. and Romaguera, S. (eds.), Optimization Problems Via Best Proximity Point Analysis, Abstract and Applied Analysis (Hindawi, New York, 2014).Google Scholar
Kirk, W. A., Srinivasan, P. S. and Veeramani, P., ‘Fixed points for mappings satisfying cyclical contractive conditions’, Fixed Point Theory 4(1) (2003), 79–89.Google Scholar
Mongkolkeha, C. and Kumam, P., ‘Best proximity point theorems for generalized cyclic contractions in ordered metric spaces’, J. Optim. Theory Appl. 155(1) (2012), 215–226.CrossRefGoogle Scholar
Samet, B., ‘Some results on best proximity points’, J. Optim. Theory Appl. 159 (2013), 281–291.CrossRefGoogle Scholar